Three positive quadratic factors bound a Vandermonde product

Proved

WorkbookSource.base_5805

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove the inequality $(x^{2}-x+1)(y^{2}-y+1)(z^{2}-z+1)\geq (x-y)(y-z)(z-x)$ for real numbers $x, y, z$ .

Source: InternLM Lean-Workbook, record lean_workbook_5805 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_5805 (x y z : ℝ) :
  (x^2 - x + 1) * (y^2 - y + 1) * (z^2 - z + 1) ≥ (x - y) * (y - z) * (z - x)  :=  by sorry

Source